Fmincon finds a minimum but Nonlinear Constraints are violated

Hello!

I'm running an optimization problem through fmincon imposing only nonlinear constraints:

options = optimset('Display','iter','Algorithm','interior-point');
[falps,Fval,EXITFLAG] = fmincon('cost_function',a_opt,[],[],[],[],[],[],'constraint',options);

Constraint is the function in with both equalities and inequalities over a_opt are defined as constraint.

Fmincon works outputting:

                                              First-order      Norm of
   Iter F-count            f(x)  Feasibility   optimality         step
      0      51    0.000000e+00    0.000e+00    1.453e-02
      1     113    9.427769e-03    0.000e+00    1.891e+02    1.376e-04
      2     166    9.427765e-03    0.000e+00    1.466e+02    2.813e-09

Local minimum possible. Constraints satisfied.

fmincon stopped because the size of the current step is less than
the default value of the step size tolerance and constraints are 
satisfied to within the default value of the constraint tolerance.

<stopping criteria details>

The details:

Optimization stopped because the relative changes in all elements of x are
less than options.TolX = 1.000000e-10, and the relative maximum constraint
violation, 0.000000e+00, is less than options.TolCon = 1.000000e-06.

Optimization Metric                                         Options
max(abs(delta_x./x)) =   7.58e-11                    TolX =   1e-10 (default)
relative max(constraint violation) =   0.00e+00    TolCon =   1e-06 (default)

With the resulting falps variables the equalities constraint are the following:

gteq =

           0
           0
           0
           0
           0
           0
           0
           0
           0
      0.6577
     -2.1498
     -2.0769
     -0.0000
     -0.0047
     -0.5568
     -0.5811
     -0.0215
      0.0000
      0.0000
     -0.0000
      0.0000
      0.0000
      0.0000
      0.0000
      0.0000
      0.0000
      0.0000
      0.0000
      0.0000
      0.0000
     -0.0000
      0.0000

Which is non zero. Why fmincon terminates? Could it be for the First-order optimality equal to e+02?

'interior-point' by definition should satisfy bounds at all iterations!

Thank you in advance for the help!

[Matt J]

Which is non zero. Why fmincon terminates?

The equality constraints will typically be non-zero when FMINCON terminates, but they should be satisfied to within the TolCon parameter which is 1e-6 by default.

Since you claim this did not happen for you, show us falps and the code for'constraint' so that we can run and reproduce gteq.

'interior-point' by definition should satisfy bounds at all iterations!

Only the ub and lb input constraints are considered 'bounds' for this purpose.

[Benjamin Bokser]

I'm having the exact same issue.

[John D'Errico]

@Benjamin: If you are having the exact same issue, then you should have read the response by MATT. Nobody else can see into your computer, to know what you might have done wrong, or to know where the problem lies. So learn to use the debugging tools, or provide sufficient information to get help.